Comparing the group theoretical approaches to the description of dipole and quadrupole collectivity in nuclei

Abstract

The comparison of the two types of collectivity in nuclear dynamics is based on the equal realizations of their basic symmetries, represented by the algebra-chain u(3) ⊃ su(3) ⊃ so(3). We illustrate this on the example of two phenomenological algebraic models: the semimicroscopic algebraic cluster model (SACM) with one of the clusters considered as a scalar and the interacting two vector boson model (IVBM). In both of them the root group structure that leads to the above chain is based on the coupling of two different U(3) representations, with different physical interpretations. These similarities allow for the use of the same mathematical tools in building the theory, but there are important differences that come from the different higher symmetries in which this equal substructures are embedded.